Self-Assessment Quiz: Simulation and Noise Models

Twenty questions. The noise-signature cluster (13–17) is the diagnostic skill. Aim for 16 or more.

Question 1

The statevector method's memory cost scales as: - A. $n$ - B. $n^2$ - C. $2^n$ - D. $4^n$

Question 2

The density-matrix method scales as: - A. $2^n$ - B. $4^n$ - C. $n^2$ - D. the same as statevector

Question 3

In the measured comparison, density_matrix first failed at: - A. 10 qubits - B. 15 qubits - C. 20 qubits - D. it never failed

Question 4

The stabilizer method's runtime on a GHZ chain from 5 to 25 qubits was: - A. exponentially growing - B. essentially flat - C. linearly growing - D. it failed above 15

Question 5

Stabilizer simulation is efficient because it tracks: - A. all $2^n$ amplitudes compactly - B. $n$ Pauli generators, about $O(n^2)$ bits - C. only the measurement outcomes - D. a random sample of the state

Question 6

A quantum computer running only Clifford gates provides: - A. exponential advantage - B. no advantage — anything it computes, a laptop computes - C. quadratic advantage - D. advantage only above 50 qubits

Question 7

Does that mean entanglement is not the resource? - A. yes - B. no — Clifford circuits generate enormous entanglement; entanglement is necessary but not sufficient - C. entanglement is irrelevant - D. Clifford circuits are not entangled

Question 8

Appending $T$ gates before a measurement did not break the stabilizer method because: - A. $T$ is a Clifford gate - B. RemoveDiagonalGatesBeforeMeasure deleted them — a diagonal gate before a $Z$ measurement changes nothing observable - C. Aer silently fell back to statevector - D. the test used too few shots

Question 9

extended_stabilizer handles $T$ gates: - A. exactly, at no extra cost - B. approximately, at cost growing exponentially in $T$ count - C. it does not handle them - D. exactly, but slowly

Question 10

Matrix-product-state simulation is efficient when: - A. qubit count is low - B. entanglement (bond dimension) stays bounded - C. the circuit is Clifford - D. there is no noise

Question 11

"MPS simulated my circuit quickly" implies: - A. nothing - B. the circuit is classically easy — a genuine finding - C. the circuit is quantum-advantageous - D. the simulator is broken

Question 12

"MPS was slow" implies: - A. the circuit is definitely quantum-advantageous - B. only that this method struggled — another may not - C. the circuit is Clifford - D. an error occurred

Question 13

Depolarizing noise on a Bell state produces: - A. impossible outcomes, with balanced peaks - B. no impossible outcomes, with tilted peaks - C. neither - D. only 00

Question 14

Readout error at $p = 0.05$ gave an error fraction of about: - A. 0.025 - B. 0.09 - C. 0.005 - D. 0.5

Question 15

Compared with depolarizing at the same $p$, readout error is: - A. about the same - B. much more damaging — roughly $2p$ versus $p/2$ - C. much less damaging - D. undetectable

Question 16

Amplitude damping ($T_1$) on a Bell state produces: - A. impossible outcomes with balanced peaks - B. no impossible outcomes, with the 00 peak growing - C. uniform noise - D. no effect

Question 17

Phase damping ($T_2$) measured in the computational basis produces: - A. a large error fraction - B. nothing visible — zero error fraction and zero imbalance - C. tilted peaks - D. an error

Question 18

To detect phase damping you must: - A. take more shots - B. measure in another basis — $\langle XX\rangle$ collapses as coherence is lost - C. use more qubits - D. it cannot be detected

Question 19

AerSimulator.from_backend(backend) gives you: - A. a connection to the real device - B. a local simulator carrying the device's basis gates, coupling map, and calibrated errors - C. an ideal simulator - D. the device's queue position

Question 20

Its main limitations are that it is: - A. slower than hardware - B. a static snapshot with independent Markovian errors — no crosstalk correlations, no drift - C. only valid for one qubit - D. approximate in the gate definitions

Answers

# Answer Why
1 C One amplitude per basis state. §11.2
2 B A matrix, not a vector — it costs the square. §11.3
3 C 9.1 s at 15 qubits, failure at 20. §11.1
4 B 297 ms at 25, same as at 5. §11.1
5 B Track the symmetries, never write down the state. §11.4
6 B Which makes it a sharp test for advantage claims. §11.4
7 B A 1000-qubit GHZ state is maximally entangled and easy. §11.4
8 B The test never presented a non-Clifford circuit. §11.4
9 B Monte Carlo over stabilizer decompositions. §11.4
10 B Cost is $O(n\chi^2)$ — linear in $n$. §11.5
11 B And it matters enormously for any advantage claim. §11.5
12 B Proving easy is easier than proving hard. §11.5
13 A Symmetric — "random" has no preferred direction. §11.7
14 B $\approx 2p$: either qubit misread is enough. §11.7
15 B Why readout mitigation leads Chapter 13. §11.7
16 B Zero impossible outcomes, +0.144 imbalance at $\gamma=0.15$. §11.7
17 B Error 0.0000, imbalance 0.0007 at any strength. §11.7
18 B Chapter 4's entanglement witness, doing its job. §11.7
19 B The most useful development practice in the chapter. §11.6
20 B Order of magnitude right, third decimal wrong. §11.6

Topic Map

Questions Topic Section If you missed these
1–4 Methods and scaling §11.1–11.3 Do Exercise 11.6 and watch density-matrix fail
5–9 Stabilizer and Clifford §11.4 Do Exercise 11.8 — the vanishing $T$ gates are the lesson
10–12 MPS §11.5 The one-way inference is the part to retain
13–18 Noise signatures §11.7 Do Exercise 11.10. This is the diagnostic skill
19, 20 Backend noise models §11.6 Build one from your own device today

Score 16+: go to Chapter 12.

Score 12–15: the signature cluster (13–18) is the one that pays off immediately. If you missed 17 or 18, reread the "channel this diagnostic cannot see" section — phase damping being invisible in the computational basis is the fifth appearance of this book's most persistent theme.

Score under 12: the scaling numbers are reference. Three things to carry into Chapter 12: AerSimulator.from_backend(), impossible outcomes vs. peak imbalance are independent axes, and the computational basis is blind to phase.